Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 899 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.Find the value of x² − 2xy + y² when x = 4 and y = 1.
2. 2.Use (a + b)(a − b) = a² − b² to find 63 × 57.
3. 3.Use a² − b² = (a + b)(a − b) to find 55² − 5².
4. 4.Use (a − b)² = a² − 2ab + b² to find 65².
5. 5.Use (a + b)(a − b) = a² − b² to find 24 × 16.
6. 6.Use (a + b)(a − b) = a² − b² to find 55 × 45.
7. 7.Use (a − b)² = a² − 2ab + b² to find 69².
8. 8.Use (a + b)² = a² + 2ab + b² to find 36².
9. 9.Use (a + b)² = a² + 2ab + b² to find 59².
10. 10.Use (a + b)(a − b) = a² − b² to find 107 × 93.
11. 11.Use (a − b)² = a² − 2ab + b² to find 79².
12. 12.Use (a − b)² = a² − 2ab + b² to find 77².
13. 13.Use (a − b)² = a² − 2ab + b² to find 89².
14. 14.If a + b = 9 and ab = 20, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 25 × 15.
16. 16.Use (a + b)(a − b) = a² − b² to find 109 × 91.
17. 17.Use (a + b)(a − b) = a² − b² to find 57 × 43.
18. 18.Use (a − b)² = a² − 2ab + b² to find 28².
19. 19.Use (a + b)(a − b) = a² − b² to find 43 × 37.
20. 20.If a + b = 4 and ab = 3, what is a² + b²?
21. 21.If a + b = 10 and ab = 21, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 46².
23. 23.Use (a + b)(a − b) = a² − b² to find 108 × 92.
24. 24.Use (a + b)(a − b) = a² − b² to find 37 × 23.
25. 25.Use (a + b)(a − b) = a² − b² to find 104 × 96.
26. 26.Use a² − b² = (a + b)(a − b) to find 50² − 1².
27. 27.Use (a − b)² = a² − 2ab + b² to find 48².
28. 28.Use a² − b² = (a + b)(a − b) to find 21² − 2².
29. 29.Use (a + b)(a − b) = a² − b² to find 78 × 62.
30. 30.If a − b = 1 and ab = 2, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 86².
32. 32.Use (a − b)² = a² − 2ab + b² to find 49².
33. 33.Use (a + b)² = a² + 2ab + b² to find 41².
34. 34.Find the value of x² + 2xy + y² when x = 13 and y = 12.
35. 35.Use (a + b)² = a² + 2ab + b² to find 13².
36. 36.Find the value of x² + 2xy + y² when x = 3 and y = 1.
37. 37.Find the value of x² − y² when x = 14 and y = 5.
38. 38.If a − b = 3 and ab = 4, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 36 × 24.
40. 40.Find the value of x² + 2xy + y² when x = 15 and y = 9.

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